What a sad development. I understand that your husband has dug in and thinks he is right to be so angry but I’d like to offer another way to look at this situation. Different people simply have differing amounts of energy to put into relationships when they have young children. Of course, I may be wrong. You know your sister-in-law and I don’t. But often enough when I dig a little deeper in situations like this, I generally find one of two things. Either the offending person is simply overwhelmed but embarrassed to admit it or, another possibility, the two sides have differing expectations of the relationship but have never talked it out.
In this case, your sister-in-law did make an effort to respond to your complaint but her letter (following the christening) wasn’t what you expected. She was cordial to you at the shower but you wanted something more. She responds to your visits but you want her to also initiate them. From her point of view, it may seem that no matter what she does, it’s not enough to satisfy her brother and you.
Ideally, it would be wonderful if your husband could talk to his sister without judgment, accusations, or anger. Instead, he could talk to her about his heartfelt wish for your two families to know each other better and to raise your collective children as cousins who know each other well and care about each other. He could ask her if she shares that wish and, if so, what she needs to make it happen. That kind of conversation would open things up instead of shutting them down.
You invited your sister-in-law to be your daughter’s godmother for good reasons. Those reasons have probably not changed. It would be a mistake to disrupt the relationship between your daughter and her aunt. It would definitely make things much, much worse. I hope you will try talking things out instead.
I wish you well.